Abstract
The direct and inverse scattering problem for the asymmetric chiral O(3)-field equation is investigated by the Gel'fand-Levitan approach. The same results for the Landau-Lifshitz equation are presented. The canonical variables are derived and the Hamiltonian perturbation theory of these equations is constructed. It is not difficult to apply the methods of the paper to any L-operator with spectral parameter on a curve of genus g > 0.
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